Practice Exercise 1: Study the information given below and answer the questions based on it.

Six persons A, B, C, D, E, and F have different weights and heights. B is taller than A and E but lighter than A and E. D is taller than B. E is only taller than C and F. Only one person lighter than A. D is heavier than C and E but not the heaviest. The number of persons heavier than F is same as shorter than him. Not more than two persons are heavier than C.

1. Who among the following is shortest in the group?

A. C

B. F

C. E

D. D

E. A

2.Who among the following is heaviest in the group?

A. D

B. C

C. F

D. B

E. E

3. How many persons are lighter than C?

A. None

B. One

C. Two

D. Three

E. Four

> B is taller than A and E but lighter than A and E.

Height: B > A, E

Weight:  A, E > B

> D is taller than B.

Height: D > B > A, E

> E is only taller than C and F.

Height: D > B > A > E > C, F

> Only one person is lighter than A.

Weight: E > A > B

> D is heavier than C and E but not the heaviest.

This implies F is heaviest.

Weight: F > D > E > A > B

> The number of persons heavier than F is same as shorter than him.

Height: D > B > A > E > C > F

> Not more than two persons are heavier than C.

Weight: F > D > C > E > A > B

Now let’s answer the questions:

1. F is the shortest in the group. So, B is the correct option.

2. F is the heaviest in the group. So, C is the correct option.

3. There are three persons: A, B, and E, which are lighter than C. So, D is the correct option.

Practice Exercise 2: Study the information given below and answer the questions based on it.

Eight persons A, B, C, D, E, F, G, and H live on an eight-floor building. The ground floor is numbered 1 and the topmost floor is numbered 8. They run in a different meters race, 4200m, 5600m, 6100m, 6800m, 7400m, 7800m, 8200m, and 9400m, but not necessarily in the same order. A, who runs 4200m, lives on an even-numbered floor below 5th floor. The ones who live on 4th and 5th floor run for a total of 12000m. Three persons live between A and C. Two persons live between C and H. Three persons live between H and the one who runs 7400m. Two persons live between G and the one who runs 5600m. D, who runs 6800m, lives above A on an odd-numbered floor. The one who lives just above D runs less than D. B lives above G. The one who lives on 3rd floor runs more than E, who runs more than F. 

1. On which floor does the person who runs the highest lives?

A. 1st

B. 2nd

C. 3rd

D. 8th

E. 5th

2. How many persons run more than B?

A. 2

B. 3

C. 4

D. 5

E. More than 5

3. Which of the following combinations is correct?

A. D – 6100m

B. C – 7th floor

C. A – 4th floor

D. E – 7400m

E. G – 4th floor

4. How many meters does H run?

A. 5600m

B. 7800m

C. 9400m

D. 8200m

E. 6100m

5. Who among the following lives on the 7th floor?

A. A

B. B

C. D

D. H

E. G

> A, who runs 4200m, lives on an even-numbered floor below 5th floor.

There are two possibilities:

Practice Exercise 2 Table (Part - 1)

> Three persons live between A and C. Two persons live between C and H. Three persons live between H and the one who runs 7400m. D, who runs 6800m, lives above A on an odd-numbered floor.

Practice Exercise 2 Table (Part - 2)

> The ones who live on 4th and 5th floor run for a total of 12000m.

This is not possible in Case 2 as no one runs a 5200m race. So, we reject this case.

Practice Exercise 2 Table (Part - 3)

> B lives above G. The one who lives on 3rd floor runs more than E, who runs more than F.

This implies E and F do not live on the 3rd floor. Therefore, G lives on the 3rd floor and B lives on the 6th floor.

> Two persons live between G and the one who runs 5600m.

> The one who lives just above D runs less than D.

This implies C runs for 6100m.

> The one who lives on 3rd floor runs more than E, who runs more than F.

This implies G runs for 9400m, E runs for 8200m and F runs for 7400m.

Practice Exercise 2 Table (Part - 4)

Now let’s answer the questions:

1. G runs for 9400m and lives on the 3rd floor. So, C is the correct option.

2. There are 6 persons who run more than B. So, E is the correct option.

3. Option (C) is correct.

4. H runs for 7800m. So, B is the correct option.

5. Option (C) is correct.

Practice Exercise 3: Each of the five friends A, B, C, D, and E travels different distances to their workplaces. A travels more than B but less than E. D travels more than only C. The one who travels the most, travels 30km. B travels 15 km to his workplace.

Who amongst the following possibly travels 5 km to the workplace?

A. A

B. C

C. D

D. E

E. Either C or D

Distance Travelled: E > A > B > D > C

E travels 30 km and B travels 15 km to the workplace. Therefore, either C or D possibly travels 5 km to the workplace. So, E is the correct option.

Practice Exercise 4: Study the information given below and answer the questions based on it.

Seven persons A, C, H, J, N, O, and V are arranged in terms of decreasing heights values but with random weights.

The height of C is 164 cm. The height of J, 161 cm is exactly in the middle. The lowest weight is 55 kg. All the weights are multiples of 5 kg. O is not the shortest but its weight is highest. H is shorter than only two persons. N’s weight is 65 kg. The lowest height is 157 cm. The person with 80 kg weight is the longest. C is shorter than only one person. V’s weight is 70 kg, which is 5 kg less than H. N is longer than both persons, one who has the highest weight and V. J does not have the lowest weight. There is a difference of 9 cm between the person highest in height and the person highest in weight.

1. What is the possible height of H?

A. 160 cm

B. 162 cm

C. 163 cm

D. Either option B or C

E. 159 cm

2. Who among the following is the third shortest?

A. O

B. N

C. H

D. None of them is true

E. Either N or O

3. Who among the following has the second-highest weight?

A. N

B. J

C. C

D. A

E. None of them

> The height of J, 161 cm is exactly in the middle. H is shorter than only two persons. The lowest height is 157 cm. The person with 80 kg weight is the longest. C is shorter than only one person. V’s weight is 70 kg, which is 5 kg less than H. 

> The height of C is 164 cm.

Practice Exercise 4 Table (Part - 1)

> O is not the shortest but its weight is highest. N is longer than both persons, one who has the highest weight and V. N’s weight is 65 kg. V’s weight is 70 kg.

Practice Exercise 4 Table (Part - 2)

> The lowest weight is 55 kg. All the weights are multiples of 5 kg. J does not have the lowest weight.

This implies C has the lowest weight. Therefore, the weight of O is 85 kg, and that of J is 60 kg.

Practice Exercise 4 Table (Part - 3)

Now let’s answer the questions:

1. Height of H would be greater than 161 cm and less than 164 cm. Therefore, it can possibly be 162 cm or 163 cm. So, D is the correct option.

2. N is the third shortest. So, B is the correct option.

3. A, who weighs 80 kg, has the second-highest weight. So, D is the correct option.

Practice Exercise 5: Read the passage given below and solve the questions based on it.

During their stint at IIM Shillong, ten students have opted for various electives named from A to F. In these electives, students are given points on a scale of 1 to 5 points. Points obtained by students can be integral points only.

It is also known that not all the electives are taken by all the students and not all the students are taking at least an elective.

The range of scores indicates the maximum and minimum scores in that elective by the students who have chosen the elective. However, if the range of the scores is 1-4, then at least one of the students must have got 1 point and at least one student must have got 4 points in that elective.

The number of elective takers out of the 10 students is given in the last column.

Question 5 Table

1. How many students have scored more than 4 points in at least 2 electives?

A. 4

B. 7

C. 2

D. Cannot be determined

2. What is the minimum number of students who must have scored less than 2 points in at least one elective?

A. 3

B. 4

C. 2

D. None of these

3. Elective C and elective E are merged to form a new elective N. This new elective N will have all those students who have opted elective C and elective E and the scores of each of these electives have been taken into consideration while finding the average of elective N. What is the average score of elective N?

A. 4

B. 3

C. 3.5

D. Cannot be determined

4. Elective A and elective B are merged to form a new elective H. This new elective H will be having all those students who have opted elective A and elective B and the scores of each of these electives have been taken into consideration while finding the average of elective H. If none of the students of elective A and elective B are common, then what will be the average score of elective H?

A. 10/3

B. 3

C. 3.5

D None of these

1. It is not possible to determine the number of students who scored more than 4 points in at least 2 electives. So, D is the correct option.

2. 

> In subject A, one student scored 1 point and the remaining five students scored 4 points each.

> In subject C, one student scored 1 point and the remaining six students scored a total of 27 points.

> In subject D, the range of scores is 1-2, the total score by the students is 4 and the number of students is 3. Therefore, two students scored 1 point each and the third student scored 2 points.

Since a student can opt for more than one elective, the minimum number of students who have scored less than 2 points in at least one elective is 2. So, C is the correct option.

3. With the information provided, we cannot determine the average marks of elective N. So, D is the correct option.

4. It is given to us that none of the students of elective A and elective B are common. Also, elective H has all those students who have opted for elective A and elective B. Therefore, the number of students in elective H = 6 + 3 = 9

Total score by students in elective A = 6 × 3.5 = 21

Total score by students in elective B = 3 × 3 = 9

Therefore, the average score of elective H = (21 + 9)/9 = 10/3

So, A is the correct option.